cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A370384 Number of permutations of [n] having no substring [k,k+1,k+2,k+3,k+4,k+5].

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%I A370384 #16 Feb 19 2024 09:56:40
%S A370384 1,1,2,6,24,120,719,5037,40306,362802,3628296,39913080,478970641,
%T A370384 6226733531,87175347936,1307641346772,20922387099240,355682119243320,
%U A370384 6402298503373917,121643960874649867,2432883613692550316,51090627024035616300,1123995015882951892680
%N A370384 Number of permutations of [n] having no substring [k,k+1,k+2,k+3,k+4,k+5].
%H A370384 Alois P. Heinz, <a href="/A370384/b370384.txt">Table of n, a(n) for n = 0..450</a>
%H A370384 D. M. Jackson and R. C. Read, <a href="http://gdz.sub.uni-goettingen.de/dms/load/img/?PID=GDZPPN002031183">A note on permutations without runs of given length</a>, Aequationes Math. 17 (1978), no. 2-3, 336-343.
%F A370384 G.f.: Sum_{k>=0} k! * ( (x-x^6)/(1-x^6) )^k.
%F A370384 a(n) = Sum_{k=0..5} A184182(n,k). - _Alois P. Heinz_, Feb 17 2024
%o A370384 (PARI) my(N=30, x='x+O('x^N)); Vec(sum(k=0, N, k!*((x-x^6)/(1-x^6))^k))
%Y A370384 Cf. A000255, A002628, A132647, A184182, A370383.
%K A370384 nonn
%O A370384 0,3
%A A370384 _Seiichi Manyama_, Feb 17 2024